Simple Linear Regression

Question 1

What is Simple Linear Regression?

Answer 1

Simple Linear Regression models the relationship between one independent variable (X) and one dependent variable (Y) using a linear equation.

Question 2

What is the mathematical equation of Simple Linear Regression?

Answer 2

The equation is Y = β0 + β1X + ε, where β0 is the intercept, β1 is the slope, and ε is the error term.

Question 3

What is the role of the slope (β1) in Simple Linear Regression?

Answer 3

The slope represents the change in the dependent variable (Y) for a one-unit increase in the independent variable (X).

Question 4

What is the role of the intercept (β0) in Simple Linear Regression?

Answer 4

The intercept is the value of Y when X is 0, representing the starting point of the regression line.

Question 5

What method is commonly used to find the best-fit line in Simple Linear Regression?

Answer 5

The Ordinary Least Squares (OLS) method minimizes the sum of squared residuals to determine the best-fit line.

Question 6

How do you implement Simple Linear Regression in Scikit-Learn?

Answer 6

from sklearn.linear_model import LinearRegression
model = LinearRegression()
model.fit(X_train, y_train)
predictions = model.predict(X_test)

Question 7

What metric is used to evaluate Simple Linear Regression?

Answer 7

R-squared (R²) measures how well the independent variable explains the variance in the dependent variable.

Question 8

What are the assumptions of Simple Linear Regression?

Answer 8

Linearity, Independence of errors, Homoscedasticity, Normality of residuals, and No significant outliers.

Question 9

What does a high R-squared value indicate?

Answer 9

A high R² value (close to 1) indicates that the model explains most of the variability in the dependent variable.

Question 10

How do you visualize a Simple Linear Regression model?

Answer 10

Using a scatter plot with the regression line: ```
import matplotlib.pyplot as plt
plt.scatter(X, y, color=’blue’)
plt.plot(X, model.predict(X), color=’red’)
plt.show()
~~~